On the structure of smooth components of Springer fibers

Lucas Fresse, Anna Melnikov, Sammar Sakas-Obeid

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincaré polynomials.

Original languageEnglish
Pages (from-to)2301-2315
Number of pages15
JournalProceedings of the American Mathematical Society
Volume143
Issue number6
DOIs
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 American Mathematical Society.

Keywords

  • Betti numbers
  • Components of a Springer fiber
  • Flag manifolds
  • Grassmannian varieties
  • Iterated bundles

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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